國立清華大學 數學系

Abstract In this talk, I will discuss the existence and qualitative properties of traveling waves for spatially periodic reaction-diffusion equations with bistable nonlinearities. The spreading theory of such equations in spatially homogeneous media is well established by Fife-McLeod (1977). However, the presence of spatial periodicity makes the problem of the existence of traveling waves rather subtle. I will focus especially on the influence of the spatial period, and discuss several existence results when the spatial period is small or large. I will also characterize the sign of the front speeds and talk about the global exponential stability and uniqueness of traveling waves with nonzero speed. This talk is based on a joint work with François Hamel and Xiao-Qiang Zhao (IUMJ, 2017).